What are the sizes of angles in a scalene triangle with given expressions?

[Frank212]

Homework Statement

The three angles of a scalene triangle are x degrees, (x-12) degrees and (2x+6) degrees. What sizes are the angles?[/B]

Homework Equations

Triangle = a+b+c =180
Scalene = no equal size or angles[/B]

The Attempt at a Solution

So what do you do with (x-12) degrees and (2x+6) degrees?
I tried putting them all in an equation to isolate x but it was an incorrect approach. I can't equally divide the triangle since it's a scalene triangle. Can someone give me a clue?
x+(x-12)+(2x+6)=180
x=93/2[/B]

 

[BvU]

Hi,

x+(x-12)+(2x+6)=180

Good. write it out using a+(b+c) = a+ b+ c etcetera...

 

[member 587159]

Your approach is right:

a + b + c = 180
=> (x-12)+(2x+6) + x = 180

Now isolate x, and verify your results by filling x in the original question.

I tried putting them all in an equation to isolate x but it was an incorrect approach. I can't equally divide the triangle since it's a scalene triangle.

What exactly do you mean by this?

 

[BvU]

Hi Frank, (a bit belated, but welcome nevertheless )
I notice you had a similar problem earlier and managed to solve it. Do you recognize that you are in the same situation with the current problem ?

Thank you ehild, your explanation really helped a lot.

45+(x+44)+(3x-23)+3x=360
7x+66=360
7x=294
7x/7=294/7
x=42

 

[Frank212]

Hi Frank, (a bit belated, but welcome nevertheless )
I notice you had a similar problem earlier and managed to solve it. Do you recognize that you are in the same situation with the current problem ?

Yeah but I'm not trying to find one variable, I'm trying to find 3 angles, according to the answers

Obviously I know the answers now but I want to understand the step by step process behind it so I can learn from it.

 

[Frank212]

Your approach is right:

a + b + c = 180
=> (x-12)+(2x+6) + x = 180

Now isolate x, and verify your results by filling x in the original question.
What exactly do you mean by this?

Thanks a lot man, I got confused but now I understand it, after isolating x I just plug it into the equation.

x: 93/2 = 46.5 degrees
(x-12): 46.5-12= 34.5 degrees
a+b+c=180
46.5+34.5=81
180-81=99 degrees